Systems and methods for providing multiple strapdown solutions in one attitude heading and reference system (AHRS)

1. An inertial navigation method of a vehicle, the method comprising:

receiving, at an integrated circuit of the vehicle, at each of a plurality of iterations, data comprising one or more physical quantities from a first three-axis sensor and a second three-axis sensor;

at each of the plurality of iterations:

determining a plurality of solutions of a roll of the vehicle, based on the data,

determining a plurality of solutions of a pitch of the vehicle, based on the data, and

determining a plurality of solutions of a heading of the vehicle based on the data; at each of the plurality of iterations:

determining a first Gaussian curve based on the plurality of solutions of the roll of the vehicle,

determining a second Gaussian curve based on the plurality of solutions of the pitch of the vehicle, and

determining a third a Gaussian curve based on the plurality of solutions of the heading of the vehicle;

at each of the plurality of iterations:

applying the first Gaussian curve to the plurality of solutions of the roll of the vehicle and weighting the plurality of solutions of the roll of the vehicle based on a position of the first Gaussian curve, thereby determining a plurality of weighted solutions of the roll of the vehicle,

applying the second Gaussian curve to the plurality of solutions of the pitch of the vehicle and weighting the plurality of solutions of the pitch of the vehicle based on a position of the second Gaussian curve, thereby determining a plurality of weighted solutions of the pitch of the vehicle,

applying third Gaussian curve to the plurality of solutions of the heading of the vehicle and weighting the plurality of solutions of the heading of the vehicle based on a position of the third Gaussian curve, thereby determining a plurality of weighted solutions of the heading of the vehicle;

at each of the plurality of iterations:

calculating a combined roll of the vehicle based on the plurality of weighted solutions of the roll of the vehicle,

calculating a combined pitch of the vehicle based on the plurality of weighted solutions of the pitch of the vehicle, and

calculating a combined heading of the vehicle based on the plurality of weighted solutions of the heading of the vehicle; and

at each of the plurality of iterations: controlling an engine of the vehicle based on the combined roll of the vehicle, the combined pitch of the vehicle, and the combined heading of the vehicle.

2. The inertial navigation method of the vehicle according to claim 1 , wherein, at each of the plurality of iterations, the controlling the engine of the vehicle comprises outputting the combined roll of the vehicle, the combined pitch of the vehicle, and the combined heading of the vehicle to a navigation system of the vehicle and the navigation system of the vehicle controlling the engine of the vehicle.

3. The inertial navigation method according to claim 1 , wherein the first Gaussian curve is a first Probability Distribution Function, the second Gaussian curve is a second Probability Distribution Function, and the third Gaussian curve is a third Probability Distribution Function.

4. A vehicle comprising:

an engine; and

as inertial navigation system comprising:

a first three-axis sensor and a second three-axis sensor configured to measure one or more physical quantities;

a memory storing instructions thereon;

a controller, operatively coupled to the first three-axis sensor and the second three-axis sensor, the controller configured to execute the instructions and thereby:

receive, at each of a plurality of iterations, data comprising the one or more physical quantities from the first three-axis sensor and the second three-axis sensor;

at each of the plurality of iterations, determine a plurality of solutions of a roll of the vehicle, determine a plurality of solutions of a pitch of the vehicle, and determine a plurality of solutions of a heading of a vehicle, based on the data;

at each of the plurality of iterations, determine a first Gaussian curve based on the plurality of solutions of the roll of the vehicle, determine a second Gaussian curve based on the plurality of solutions of the pitch of the vehicle, and determine a third Gaussian curve based on the plurality of solutions of the heading of the vehicle;

at each of the plurality of iterations, apply the first Gaussian curve to the plurality of solutions of the roll of the vehicle, apply the second Gaussian curve to the plurality of solutions of the pitch of the vehicle, and apply the third Gaussian curve to the plurality of solutions of the heading of the vehicle;

at each of the plurality of iterations:

weigh the plurality of solutions of the roll of the vehicle based on a position on the first Gaussian curve, thereby determining a plurality of weighted solutions of the roll of the vehicle,

weigh the plurality of solutions of the pitch of the vehicle based on a position on the second Gaussian curve, thereby determining a plurality of weighted solutions of the pitch of the vehicle, and

weigh the plurality of solutions of the heading of the vehicle based on a position on the third Gaussian curve, thereby determining a plurality of weighted solutions of the heading of the vehicle;

at each of the plurality of iterations calculate a combined roll of the vehicle, a combined pitch of the vehicle, and a combined heading of the vehicle based on the plurality of weighted solutions of the roll of the vehicle, the pitch of the vehicle, and the heading of the vehicle; and

at each of the plurality of iterations, control the engine based on the combined roll of the vehicle, the combined pitch of the vehicle, and the combined heading of the vehicle.

5. The vehicle according to claim 4 , further comprising:

a navigational display;

wherein, at each of the plurality of iterations, the controlling the engine comprises outputting, to the navigational display, the combined roll of the vehicle, the combined pitch of the vehicle, and the combined heading of the vehicle; and

wherein the navigational display is configured to control the engine based on the combined roll of the vehicle, the combined pitch of the vehicle, and the combined heading of the vehicle.

6. The inertial navigation system according to claim 4 , wherein the first Gaussian curve is a first Probability Distribution Function, the second Gaussian curve is a second Probability Distribution Function, and the third Gaussian curve is a third Probability Distribution Function.